DOPPLER SHIFT CCEA GCE Physics Unit AS 2: 2.7 Astronomy

Objective

To demonstrate how the Doppler shift can be used to measure the motion of a planet orbiting a star.

Introduction

When a light source, such as a planet, star or galaxy, moves towards or away from an observer, the light waves will be scrunched up or stretched out so that they appear bluer or redder. This is the Doppler effect, and corresponds to a change in wavelength of the light. The wavelength change is proportional to relative motion along the line of sight. To measure it, we need to know the wavelength of both emitted light and received light. Light is absorbed and emitted by atoms at precise wavelengths, corresponding to lines in the spectrum. By measuring the wavelength of a known line, we can calculate the red shift. The relative shift in wavelength is then equal to the radial velocity relative to the speed of light.

Figure 1. The visible light emitted by different types of star as viewed through a spectroscope. Wavelength runs from left (blue) to right (red) The spectral type of each star is shown on the left, and the star’s surface temperature is shown on the right. The Sun is a G star. The hottest stars show a blue colour and strong dark lines due to atomic hydrogen. F and G stars are mode yellow, and show a the veil of faint atomic lines. Cool stars are red and shows bands due to molecules. Credit: Michael Lemke. Source: http:/www.arm.ac.uk/~csj/articles.popular/spectra/spek.html

Armagh Observatory and Planetarium Doppler Shift: Exercise 1 : 2018 March 21

DOPPLER SHIFT !2

Experiment

Figure 1 shows how the spectra of various types of star appear when viewed through a spectroscope. A planet in orbit around a star reflects starlight, with a spectrum similar to its parent star. By measuring the red shift of the planet’s spectrum, we can find the period and orbital velocity of the planet. Figure 2 shows a series of fifteen ‘observations’ of an exoplanet, centered on a line with rest wavelength λ0 = 500 nm and spread over 16 days.

Step 1

For each spectrum in Figure 2, find the darkest line in the spectrum and measure its wavelength in nanometers off the y-axis. Enter these values in Table 1.

© Armagh Observatory and Planetarium 2018

Exoplanet SpectraW

avel

engt

h (n

m)

499.7

499.8

499.9

500.0

500.1

500.2

500.3

Spectrum

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

DOPPLER SHIFT !3

© Armagh Observatory and Planetarium 2018

Radial velocities measured from Doppler shift

velo

city

(km

/s )

-100

-80

-60

-40

-20

0

20

40

60

80

100

time (day)0 2 4 6 8 10 12 14 16

spectrum time wavelength delta velocity

(day) (nm) (nm) (km s-1)

— 500.00 — x c/λ0 = 600 (km s-1 nm-1)

1 0.20 500.03 0.03 18

2 1.18 500.13 0.13 78

3 2.104 2.905 3.806 4.207 5.158 7.009 9.00

10 9.9011 11.8712 13.8013 14.2014 15.1015 15.82

Table 1

DOPPLER SHIFT !4

Step 2

Calculate δλ = λ - λ0 and enter these values in Table 1. Convert these numbers to red shifts using the Doppler formula v = c . (λ - λ0) / λ0. Since λ0 = 500 nm and c = 300,000 km s-1, this means multiplying by c / λ0 = 300,000 / 500 = 600 km s-1 nm-1 to find velocity in km s-1. Take care with minus signs!

Step 3

Plot the velocities against the time of observation on the graph provided (the first two points are given; the time-values are also marked).

Step 4

Discuss what the plot of velocity against time can tell you. Estimate the period and amplitude of the variation.

Points for Discussion

Which points on the graph correspond to the planet moving towards the observer ?

Where on the graph is the planet crossing in front of the star ?

How will the spectrum of the planet change in brightness during its orbit ?

How easy do you think it would be to make an observation like this ? Why ?

Will these observations help to measure the mass of the planet or the star ?

Do you think that the star will also show periodic red shifts ?

Will they be larger or smaller than those of the planet ?

© Armagh Observatory and Planetarium 2018